# Singular

##### 7.7.7.0. lpKDim

Usage:
lpKDim(G[,degbound, n]); G an ideal, degbound, n optional integers

Return:
int, the K-dimension of the factor algebra

Purpose:
Computing the K-dimension of a factor algebra, given via an ideal

Assume:
- basering is a Letterplace ring. G is a Letterplace ideal.
- if you specify a different degree bound degbound,
degbound <= attrib(basering,uptodeg) should hold.

Note:
- If degbound is set, there will be a degree bound added. 0 means no
degree bound. Default: attrib(basering, uptodeg).
- n is the number of variables, which can be set to a different number.
Default: attrib(basering, lV).
- If the K-dimension is known to be infinite, a degree bound is needed

Example:
 LIB "fpadim.lib"; ring r = 0,(x,y),dp; def R = makeLetterplaceRing(5); // constructs a Letterplace ring setring R; // sets basering to Letterplace ring ideal G = x(1)*x(2), y(1)*y(2),x(1)*y(2)*x(3); // ideal G contains a Groebner basis lpKDim(G); //procedure invoked with ring parameters ==> 6 // the factor algebra is finite, so the degree bound given by the Letterplace // ring is not necessary lpKDim(G,0); // procedure without any degree bound ==> 6